2x+1/(x+2)(x-3) Find B? A?

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Bert Cushman asked Feb 14, 2022

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33 votes

2x+1/(x+2)(x-3)
Find B? A?

Mathematics
college

Bert Cushman asked Feb 14, 2022

by Bert Cushman

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1 Answer

26 votes

Explanation:

$(2x + 1)/((x + 2)(x - 3))  \equiv (A)/((x - 3))  +  ( B)/((x + 2))  \\  \\ 2x + 1 \equiv \: A(x + 2) + B(x - 3) \\ 2x + 1 \equiv \: Ax + 2A + Bx - 3B \\A +  B = 2...(1) \\ 2A - 3B = 1...(2) \\ A = (7)/(5) \: and \: B = (3)/(5) \\ (2x + 1)/((x + 2)(x - 3))  \equiv ((7)/(5))/((x - 3))  +  ( (3)/(5) )/((x + 2))$